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Stunning Dillard solar ratio

Monday, August 14th, 2017

[ by Charles Cameron — mathematics and metaphor, a ratio of the irrational ]
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A total solar eclipse in Svalbard, Longyearbyen, Norway, on March 20, 2015 — Jon Olav Nesvold

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From Annie Dillard’s Classic Essay: ‘Total Eclipse’:

Seeing a partial eclipse bears the same relation to seeing a total eclipse as kissing a man does to marrying him.

Annie Dillard is one of our great stylists, so it’s perhaps not surprising she came up with this jaw-dropping piece of mathematics, or should I call it logic? It’s a ratio, anyhow:

Seeing a partial eclipse : seeing a total eclipse :: kissing a man : marrying him

By common consent, ratios are usually applied to quantifiables — but there’s really no quantifying seeing, kissing, or marrying.

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I don’t think I’ll be able to make the eclipse, but if any of you can, please do. No less an authority than Annie Dillard — she wrote Pilgrim at Tinker’s Creek and Holy the Firm — strongly advises it.

Numbers by the numbers: three .. in Congress

Wednesday, May 3rd, 2017

[ by Charles Cameron — bipartisan Congress trumps Trump ]
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Grasping the meaning of pop lyrics isn’t my forte, but this song’s title, Two Against One, fits with the point I’m making in this post..

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I’ve talked about three-way games in Numbers by the numbers: three / pt 1, Of games III: Rock, Paper, Tank and Spectacularly non-obvious, I: Elkus on strategy & games — and very likely elsewhere —

— ah yes, in Spectacularly non-obvious, 2: threeness games, where I describe my own three-way game in a hotel swimming pool.

Today brought us a significant three-way play in Congress:

Why Congress’s Bipartisan Budget Deal Should Make Trump Worried

By cutting a bipartisan spending compromise among themselves, Republicans and Democrats in Congress not only prevented the White House from delivering on President Trump’s priorities in his very first budget, they also drafted a handy blueprint for circumventing the Trump administration in the future.

It was an outcome that should worry the new president even though Mr. Trump will be spared the humiliation of a government shutdown early in his tenure if he signs the legislation.

“We were sort of a united front, Republicans and Democrats, opposed to Trump,” said Senator Chuck Schumer of New York, the Democratic leader, in an interview.

Not exactly the words a president wants to hear in the opening months of his term — that the two usually warring parties on Capitol Hill instead joined forces to gang up on him. But that is essentially what happened.

Republicans, protective of their spending priorities, chose to cooperate with Democrats in the House and Senate to work out a five-month package they could all live with, ignoring demands from the White House for deep spending cuts in areas like environmental protection.

By insisting on proposals that both parties on Capitol Hill knew could not pass — the border wall funding in particular — the White House took itself out of the game and ceded power to Congress. Members of both parties, freed to direct money to favored initiatives, eagerly seized the opportunity and increased funding for agencies such as the National Institutes of Health rather than cutting it.

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And here’s my swimming pool game, with commentary, by way of comparison:

The idea is simplicity itself, putting it into words unambiguously is difficult.

Yesterday I was at a hotel swimming pool where two sons of another guest and my own son Emlyn were playing around together, all aged around 10-12, with nobody else there, and I asked them to play a game where one of the three would be “top guy” and the other two would try to dunk and generally overthrow him, and as soon as it became clear that the top guy had been dunked and dethroned, there would be a new “top guy” (one of the two who had been doing the overthrowing and come out the obvious winner) and the other two would pounce on him…

They were not evenly matched, but any one of them was easily outmatched by the other two working together, and being “top guy” meant your head was above water and you were, so to speak, “comfortable” — so there was a real premium on being “top guy”, and the other two were (at any time) eager to collaborate to get the position.

And there was no tendency for the two brothers to gang up against my son, because the immediacy of two defeating one was more urgent and compelling than any ideas of teaming by kinship interests, minor differences in strength and skill, etc…

From maps to graphs and back, from life to death and eternity?

Wednesday, April 19th, 2017

[ by Charles Cameron — graphs and networks, life and death, quality and quantity of life, personal mortality, the (implictly immortal) trinity ].
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I was struck by these items, verbal and visual, in Numberphile‘s YouTube video, The Four Color Map Theorem. The speaker introduces a simple, four color map:

Then indicates:

I’ve turned that map into a network:

The question, can this map be colored using four colors, or better? is the same question as saying, can this network be colored using four colors, or better?

There are things we can learn now about maps, by studying networks instead. .. By studying networks, we can study all the different kind of maps. Now, all maps make networks, but not all networks make valid maps.

Given that my HipBone game boards are graphs — my games as played are conceptual graphs — I’m always on the lookout for easily digested gobbits of graph theory to see if they’re applicable to my games, or to put that another way, whether they can startle me into any new insights.

  • At least some HipBone games could be played on maps..
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    One could thus view maps of the various sectarian interests in play in the Levant / Shams — theologies onto geographic areas, Alevi, Twelver, Salafi, Salafi-jihadist, Yezidi, Druze, Christian etc — as conceptual maps analogous to conceptual graphs.

    And these conceptual maps are important in terms of strategy.

    Different graphs could be obtained by articulating the linkages between different sects and ethnicities, eg Turkomen with Turks, Alevi and Ismaili with Twelver Shiism, and Shia with Sunni vs (eg) Christian.. and switching back and forth between map and grapoh might then prove suggestive, instructive..

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    Once started on Numberphile’s math-curious videos it can be hard to stop.. Here’s a surprise from the third such video I chased thids afternoon, the one on The Feigenbaum Constant:

    Life and Death can be mathematized!

    I think that diagram — if it can be believed — answers the vexed issue of quality and quantity, and possibly also the hard problem in consciousness.

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    I naturally attempted to place myself on the implicit timeline between Life and Death on that diagram. I’m reasonably far along (minor stroke, check, triple bypass, check, on dialysis, check, etc), and, shall we say, somewhat aware of my mortality.

    Someone get me a slide-rule, I’d like to calculate the precise.. unh, on second thoughts, maybe not.

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    The only happily viable move from here — I believe — is to infinity, so let’s go.

    My games, I’d suggest, make a contribution to graph theory. Specifically, to that branch of graph theory in which Margaret Masterman was a pioneer, is the area of conceptual graphs, which I meantioned above. Indeed, the (theo)logical icon Masterman explored with her Benedictine Abbess friend as described in Theism as a Scientific Hypothesis (part 1), Theoria to Theory Vol 1, 3rd Quarter, April 1967, pp 240-46:

    visiting it in Boolean terms:

    is none other than the graph used as an exemplar of the map-graph correlation in the Numberphile video, second illustration at the top of this post.

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    In the Trinitarian version of this graph, however, two kinds of “edge” or linkage are required: for the links between individual Persons (“non est”) and the links between Persons and Godhead (“est”).

    And the same is true, interestingly enough, with even more types of linkage, in Oronce Fine‘s (entirely secular?) map of the elements:

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    And that’s enough thinking for one day, perhaps. We shall see..

    Mes Aynak, Afghanistan, the equation

    Monday, April 10th, 2017

    [ by Charles Cameron — a question of value ]
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    Footprints: Saving artefacts in Afghanistan

    The Buddha rests quietly in a corner of the National Museum of Afghanistan.

    While a group of Afghan restorers — with more than four decades of experience between them — work to restore similar artefacts, the Buddha, dating back to at least the second century BC, sits cross-legged, arms folded, awaiting its public debut in the city.

    The statue, set to be unveiled to the public in the coming weeks, is a testament to the rich history of a nation that has seen various empires and conquerors pass through its land.

    “There are artefacts in every corner of this country,” said Fahim Rahimi, the director of the National Museum of Afghanistan. However, even the layers of sand, silt and time have not been able to keep these artefacts safe from the forces of conflict and capitalism.

    [ .. ]

    The Buddha itself, discovered near the nation’s largest copper mine, is an embodiment of the duelling threats facing the physical remnants of Afghanistan’s cultural history. The statue, sitting in a reconstructed stupa, was found in 2012 in the Mes Aynak area of the eastern province of Logar. Mes Aynak, meaning literally “the little copper source,” is home to a 2,000-year-old Buddhist city filled with ancient statues, manuscripts, frescoes, shrines and stupas. It is also at the centre of a $3billion Chinese mining contract signed in 2007.

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    William Bruce My NameSake and presumed Clansman Cameron wrote “Not everything that can be counted counts, and not everything that counts can be counted.”

    Equation implies equals. Here we have a tug of cash-and-peace.

    Trump, Flynn and immunity

    Friday, March 31st, 2017

    [ by Charles Cameron — tweets, and how they become, for me, a problem in number theory ]
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    The initial question is, should I pair this:

    with this:

    Or this:

    — or the last two with each other?

    Such are the hazards of imprisonment within the DoubleQuote system — two, when three or more are available and relevant, becomes a constraint rather than a facilitation. So would any other positive integer — and god save us from the irrationsals!


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